Fuchsian bispectral operators

The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are all Darboux transformations of powers of generalised Bessel operators (in the terminology of q-alg/9602011). For this reason they can be effectively parametrised by the points of a certain (infinite) family of algebraic manifolds as pointed out in q-alg/9602011.Comment: 32 pages, late

Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy

In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of its Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving $e^{\partial_x}$ and $\tau(t)$.Comment: 29 pages, to appear Journal of Mathematical Physics(2010

Seiberg-Witten Theory and Extended Toda Hierarchy

The quasiclassical solution to the extended Toda chain hierarchy, corresponding to the deformation of the simplest Seiberg-Witten theory by all descendants of the dual topological string model, is constructed explicitly in terms of the complex curve and generating differential. The first derivatives of prepotential or quasiclassical tau-function over the extra times, extending the Toda chain, are expressed through the multiple integrals of the Seiberg-Witten one-form. We derive the corresponding quasiclassical Virasoro constraints, discuss the functional formulation of the problem and propose generalization of the extended Toda hierarchy to the nonabelian theory.Comment: 32 pages, LaTe

Uvoz nerastova - kontrola semena i mogućnost reklamacije

Serbia is one of the countries with the continuous import of breeding sows and boars. Boars are usually imported at the age of 4 to 6 months, in the period when the quality of the breeding males cannot be determined due to sexual immaturity (prepubertal and pubertal age). In this paper, the method and results of semen quality control in 40 imported young boars are described, and also the method of documenting the cause for action claim. In the case of suspicious semen quality it is necesseary to perform at least 3 consecutive controls in one month intervals in order to establish a final estimation of quality and usability of semen. Of 40 imported boars, 4 boars (10%) were subject of complaint due to: azoospermia (1 boar), absence or reduction of total and progressive motility, present sperm agglutination (2 boars), and increased number of pathological forms of spermatozoa (78%, 1 boar). Increased proportion of sperm with unstable chromatin structure (SCSA test - 33.2% and 37.1%) was established in two boars. To initiate the complaint it is necessary to have a sales contract that provides possibility for the reclamation, recognized methods of semen quality control and trustful business relationship between all interested parties.Srbija se svrstava u red zemalja sa kontinuiranim uvozom priplodnih nazimica i nerastova. Nerastovi se uglavnom uvoze u dobi od 4 do 6 meseci, u periodu kada se kvalitet priplodnjaka ne može pouzdano utvrditi usled polne nezrelosti (prepubertetsko ili pubertetska dob nerastića). U ovom radu opisan je postupak i rezultati kontrole kvaliteta semena kod 40 mladih nerastova iz uvoza, kao i način dokumentovanja razloga za pokretanje postupka reklamacije. Kod sumnjivog kvaliteta semena potrebno je izvršiti najmanje 3 uzastopne kontrole u razmaku od po mesec dana, kako bi se donela konačna ocena o kvalitetu semena i upotrebljivosti nerasta za priplod. Od 40 uvezenih nerastova, 4 su reklamirana (10%) usled: azoospermije (1 nerast), odsustva ili smanjenje ukupne ili progresivne pokretljivosti, uz prisustvo aglutinacija spermatozoida (2 nerasta), i povećanog broja patoloških formi spermatozoida (78%; 1 nerast). Kod dva nerasta zabeležen je povećan udeo spermatozoida sa nestabilnom strukturom hromatina (SCSA test - 33,2% i 37,1%). Za pokretanje reklamacije neophodno je imati kupoprodajni ugovor koji predviđa mogućnost reklamacije, priznate metode kontrole semena kao i izgrađen poslovni odnos poverenja zainteresovanih strana

Comparative investigations of immune response of calves at different intervals between primary and secondary immunization using inactivated bovine herpes virus 1 vaccine

Bovine herpesvirus 1 (BHV-1) is one of the most siginificant causes of infections of the respiratory tract of cattle and immunoprophylaxis has a key role in curbing this infection. The intensity of the immune response against BHV-1 following immunization using inactivated commercial vaccines varies depending on the type of vaccine, but it is generally believed that they provide good protection from the development of the clinical form of the infection, and that they are safe. The paper present the development of the humoral immune response in fattening calves that were immunized against bovine herpesvirus 1 (BHV-1) at different time intervals between the primary and the secondary immunization. Calves were administered a commercial vaccine, and then they were divided into two groups which were revaccinated on days 14 or 21. Over a course of the 120 days of the duration of the experiment, blood and nasal mucus were sampled 11 times. The blood serum samples were examined for antibodies to BHV-1 using the virus neutralization (VN) test, and the nasal mucus samples were analyzed using the VN test and the ELISA method. Following revaccination, it was established that there was an increase in the antibody titer in blood of all experimental animals, and it was maintained at a high level up until the very end of the experiment (day 120). In the blood serums, maximum mean values for the antibody titer were determined on day 30 in the group that was revaccinated on day 14, and on day 45 in the group of calves revaccinated on day 21. In nasal mucus, antibodies were established at the earliest, using the virus neutralization test, on day 14 following vaccination, and using the ELISA method only after revaccination. The highest antibody titer in nasal mucus was established on day 45 in the group revaccinated on day 21, and on day 120 in the group revaccinated on day 14. Based on the established antibody titer values, calves can be revaccinated using the inactivated BHV-1 vaccine already on day 14. [Projekat Ministarstva nauke Republike Srbije, br. 31084

The local Gromov-Witten theory of CP^1 and integrable hierarchies

In this paper we begin the study of the relationship between the local Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory. Our main tool is the application of Dubrovin's formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz-Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g<=1; our methods are based on establishing, analogously to the case of KdV, a "quasi-triviality" property for the Ablowitz-Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing it successfully in the primary sector for g=2.Comment: 30 pages; v2: an issue involving constant maps contributions is pointed out in Sec. 3.3-3.4 and is now taken into account in the proofs of Thm 1.3-1.4, whose statements are unchanged. Several typos, formulae, notational inconsistencies have been fixed. v3: typos fixed, minor textual changes, version to appear on Comm. Math. Phy

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.Comment: 37 pages, 3 figures, V2: the published versio

The Extended Bigraded Toda hierarchy

We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are $\epsilon$-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix theory we give the bihamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions. Finally we study the dispersionless limit and its connection with a class of Frobenius manifolds on the orbit space of the extended affine Weyl groups of the $A$ series.Comment: 32 pages, corrected typo

Double Ramification Cycles and Integrable Hierarchies

In this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to the Dubrovin–Zhang hierarchy by a Miura transformation, and we check it in several examples